This study examined the performance of a hemispherical point-absorber wave energy converter (WEC) with a hydraulic power take-off (PTO) system. The hydraulic PTO system for power generation was modeled as an approximate coulomb damping force, which was recently proposed to reduce numerical error. To examine the hydrodynamic performance of the WEC, a three-dimensional frequency-domain numerical wave tank technique was adopted, in which the wave radiation problem and diffraction problem for a hemispherical buoy were solved in succession to obtain the hydrodynamic coefficients. The Cummins equation was also adopted to simulate the buoy displacement and extracted wave power in the time domain. For comparison, a three-dimensional wave tank experiment was conducted. Various viscous damping and energy loss from WEC system and hydraulic cylinder pressure of the PTO system were measured from the experimental results, and these values were added to the governing equation of buoy motion. Therefore, the final numerical model of the WEC system contained the viscous damping and hydraulic PTO forces as well as the potential-flow-based hydrodynamic coefficients. Using the developed numerical model, the hemispheric buoy displacement and extracted wave power were calculated for various hydraulic pressures and input wave conditions to determine the optimal conditions for the maximum wave power.